Pith. sign in

REVIEW 2 cited by

Existence and regularity in the fully nonlinear one-phase free boundary problem

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2501.12101 v1 pith:LEUEGFW6 submitted 2025-01-21 math.AP

Matteo Carducci , Bozhidar Velichkov This is my paper · ORCID
classification math.AP
keywords freeboundaryregularityexistencefullynonlinearone-phaseviscosity
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We consider viscosity solution to one-phase free boundary problems for general fully nonlinear operators and free boundary condition depending on the normal vector. We show existence of viscosity solutions via the Perron's method and we prove $C^{2,\alpha}$ regularity of flat free boundaries via a quadratic improvement of flatness. Finally, we obtain the higher regularity of the free boundary via an hodograph transform.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Smoothness and stability in the Alt-Phillips problem

    math.AP 2025-07 conditional novelty 8.0 of 10

    For the Alt-Phillips free boundary problem, the paper proves smoothness of regular free boundaries for all exponents, derives a stability inequality for negative exponents, and rules out nontrivial axially symmetric s...

  2. Free boundary regularity for a tumor growth model with obstacle

    math.AP 2025-07 accept novelty 7.0 of 10

    For a one-phase tumor growth free boundary problem with an obstacle, viscosity solutions exist and the free boundary is analytic in the interior and C^{1,α} at contact points under a non-degeneracy condition.

Pith tools